Recent advances in the theory and modelling of RF heating in inhomogeneous plasmas

Theoretical and numerical modelling of rf heating in inhomogeneous plasmas is discussed. (1) A case is examined near the lower hybrid resonance where two turning points are encountered near one another, first from a cold to a warm wave and then from the warm wave to an ion Bernstein mode. This leads to a sixth order equation which is difficult to solve as it has a quadratic coefficient. (2) Improved a symptotic representations are presented whose accuracy is crucial to the numerical solution of this type of equation. (3) A new method of exact order reduction for higher order equations with no approximations permits generation of a numerical Green function by integrating only second order equations. The differential equation is factored with an asymptotically small source term. The resulting integral equation is more easily solved. (4) A formalism for determining the 2-D structure of the wave fields and the associated power deposition profiles within the mode conversion-absorption layer has been developed by applying the parabolic approximation method to the linearized Vlasov-Maxwell equations. The new method reduces the problem to the solution of one fourth order equation and an associated parabolic diffusion type equation. (5) Time dependent transport simulations of ICRF heated discharges in tokamaks with circular and non-circular cross-sections are presented. The simulations are obtained by interfacing the WHIST 2-D MHD equilibrium and a 1-D flux surface averaged transport code with a ray tracing algorithm. (author)